Consider the following two players game:
Giving chessboard NxN, and single king placed on some square on the board. Each player in his turn, can move the king in each direction in the same way player can move king in regular chessboard game. But - the king can't return to square he was already in. Edit: the winner is the player who makes the last turn.
The question:
What is the winning strategy? Should I play first or second and what is the invariant condition?
What I discoverd so far:
if N=2 I want to be first. if N=3 and the king at first is in the middle sqaure (2,2), then I want to be second.